Simplify: (p ∨ q) ∧ (p ∧ (p ∧ q)) <=> (p ∧ q)
Showing the steps and the laws of logic used to simplify. And state why the statement as a whole is true.
2006-10-22 03:52:49 · 13 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Yes I can do it!!! I wanted to see if I was right!!
Simplify:(p ∨ q) ∧ (p ∧ (p ∧ q)) (p ∧ q)
(p ∧ (p ∧ q)) can become: ((p ∧ p) ∧ q) this is the associate law as brackets can be moved.
This new expression is simplified through the idempotent law making ((p ∧ p) ∧ q) become ((p) ∧ q) the inner brackets are then removed.
Next:(p ∨ q) ∧ (p ∧ q) (p ∧ q)
Using the Associate Law this can become:
(p ∨ (q ∧ p ∧ q)) (p ∧ q)
From this new expression (q ∧ p ∧ q) can be simplified to (p ∧ q) [since q ∧ q q]. Therefore:
(p ∨ (p ∧ q)) (p ∧ q)
Using the Absorption Law this is simplified to:
p (p ∧ q)
Which is true as (p ∧ q) can only be true when p is true and is false when p is false therefore p is equivalent to (p ∧ q).
2006-10-22 04:00:50 · update #1
The squares above are <=> it was copied from word to here and Yahoo doesn't support the character which represents <=>
2006-10-22 04:01:49 · update #2
yes, that is right
Draw ven graphs to simplfy this relationship.
if we consider that: U=p^q
then U is contained in P, q, and P V q
so the inetesection with any of them with U gives U too
OK.......
2006-10-22 04:02:14 · answer #1 · answered by mozakkera 2 · 2⤊ 2⤋
That is so easy!!!! Done that kind of algebra at the age of 11 and I hated it then and I hate it now but can still do it. You will only learn the answer if you do it by yourself. Use the law of logic!!!
2006-10-22 11:04:22 · answer #2 · answered by PATRICIA L 3 · 0⤊ 1⤋
Final Answer is 1
2006-10-22 11:05:02 · answer #3 · answered by Santhosh S 5 · 0⤊ 2⤋
Yes it is simple
But you have to do your own homework or else you will never learn
2006-10-22 10:55:54 · answer #4 · answered by ger72k 2 · 0⤊ 1⤋
Urh?
2006-10-22 11:01:12 · answer #5 · answered by pizza1512 2 · 0⤊ 1⤋
y
2006-10-22 11:02:03 · answer #6 · answered by jaeck76 3 · 0⤊ 2⤋
No, sorry
2006-10-22 10:56:12 · answer #7 · answered by Bruce P 7 · 0⤊ 1⤋
Yawn...,sorry,no idea...
2006-10-22 10:55:14 · answer #8 · answered by Fudgie 6 · 0⤊ 1⤋
(p ⨠q) ⧠(p ⧠(p ⧠q)) <=> (p ⧠q)=b-llocks
simple enough for you?
2006-10-22 11:14:10 · answer #9 · answered by ? 2 · 0⤊ 2⤋
no and why should i want to
2006-10-22 11:00:23 · answer #10 · answered by Anonymous · 0⤊ 2⤋